The Katz Centrality
Learn the Katz centrality, an extension of the eigenvector centrality for directed graphs that solves a problem for nodes with an in-degree of zero.
A problem with eigenvector centrality
Eigenvector centrality has a nice intuition of grabbing the importance from the neighbors of a node in order to determine its importance. However, for directed graphs, we can end up with a problem when we have nodes with an in-degree equal to zero.
In the case of an in-degree of zero, the importance of that node is going to be zero (or very close to it). Therefore, it will pass a zero value for its neighbors, making their eigenvector centrality become way smaller. If a node receives a connection only for a node with zero in-degree, then this node will also be zeroed.
This phenomenon is called zero-propagation, and it is something we want to avoid. Let’s look at an example of this:
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